# perf_mod: Bayesian Analysis of Resampling Statistics In topepo/tidyposterior: Bayesian Analysis to Compare Models using Resampling Statistics

## Description

Bayesian analysis used here to answer the question: "when looking at resampling results, are the differences between models 'real?'" To answer this, a model can be created were the outcome is the resampling statistics (e.g. accuracy or RMSE). These values are explained by the model types. In doing this, we can get parameter estimates for each model's affect on performance and make statistical (and practical) comparisons between models.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```perf_mod(object, ...) ## S3 method for class 'rset' perf_mod(object, transform = no_trans, hetero_var = FALSE, formula = NULL, ...) ## S3 method for class 'vfold_cv' perf_mod(object, transform = no_trans, hetero_var = FALSE, ...) ## S3 method for class 'resamples' perf_mod( object, transform = no_trans, hetero_var = FALSE, metric = object\$metrics, ... ) ## S3 method for class 'data.frame' perf_mod(object, transform = no_trans, hetero_var = FALSE, formula = NULL, ...) ```

## Arguments

 `object` A data frame or an `rset` object (such as `rsample::vfold_cv()`) containing the `id` column(s) and at least two numeric columns of model performance statistics (e.g. accuracy). Additionally, an object from `caret::resamples` can be used. `...` Additional arguments to pass to `rstanarm::stan_glmer()` such as `verbose`, `prior`, `seed`, `family`, etc. `transform` An named list of transformation and inverse transformation functions. See `logit_trans()` as an example. `hetero_var` A logical; if `TRUE`, then different variances are estimated for each model group. Otherwise, the same variance is used for each group. Estimating heterogeneous variances may slow or prevent convergence. `formula` An optional model formula to use for the Bayesian hierarchical model (see Details below). `metric` A single character value for the statistic from the `resamples` object that should be analyzed.

## Details

These functions can be used to process and analyze matched resampling statistics from different models using a Bayesian generalized linear model with effects for the model and the resamples.

By default, a generalized linear model with Gaussian error and an identity link is fit to the data and has terms for the predictive model grouping variable. In this way, the performance metrics can be compared between models.

Additionally, random effect terms are also used. For most resampling methods (except repeated V-fold cross-validation), a simple random intercept model its used with an exchangeable (i.e. compound-symmetric) variance structure. In the case of repeated cross-validation, two random intercept terms are used; one for the repeat and another for the fold within repeat. These also have exchangeable correlation structures.

The above model specification assumes that the variance in the performance metrics is the same across models. However, this is unlikely to be true in some cases. For example, for simple binomial accuracy, it well know that the variance is highest when the accuracy is near 50 percent. When the argument `hetero_var = TRUE`, the variance structure uses random intercepts for each model term. This may produce more realistic posterior distributions but may take more time to converge.

Examples of the default formulas are:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ``` # One ID field and common variance: statistic ~ model + (model | id) # One ID field and heterogeneous variance: statistic ~ model + (model + 0 | id) # Repeated CV (id = repeat, id2 = fold within repeat) # with a common variance: statistic ~ model + (model | id2/id) # Repeated CV (id = repeat, id2 = fold within repeat) # with a heterogeneous variance: statistic ~ model + (model + 0| id2/id) # Default for unknown resampling method and # multiple ID fields: statistic ~ model + (model | idN/../id) ```

Custom formulas should use `statistic` as the outcome variable and `model` as the factor variable with the model names.

Also, as shown in the package vignettes, the Gaussian assumption make be unrealistic. In this case, there are at least two approaches that can be used. First, the outcome statistics can be transformed prior to fitting the model. For example, for accuracy, the logit transformation can be used to convert the outcome values to be on the real line and a model is fit to these data. Once the posterior distributions are computed, the inverse transformation can be used to put them back into the original units. The `transform` argument can be used to do this.

The second approach would be to use a different error distribution from the exponential family. For RMSE values, the Gamma distribution may produce better results at the expense of model computational complexity. This can be achieved by passing the `family` argument to `perf_mod` as one might with the `glm` function.

## Value

An object of class `perf_mod`.

topepo/tidyposterior documentation built on July 5, 2020, 11:11 p.m.